    The final test considered in this paper is the two-dimensional
double mach reflection problem[1]} where a vertical shock
wave moves horizontally into a wedge that is inclined by some angle.
The computational domain for this problem is chosen to be \([0,4]\times [0,1],\) 
and the reflecting wall lies at the bottom of the computational domain
for \(\frac{1}{6}\le x\le 4\) . Initially a right-moving Mach 10
shock is positioned at \(x=\frac{1}{6},y=0,\)  and makes a \(60^{o}\) 
angle with the x-axis. For the bottom boundary, the exact postshock
condition is imposed for the part from \(x=0\)  to \(x=\frac{1}{6}\) 
and a reflective boundary condition is used for the rest. The top
boundary of our computational domain uses the exact motion of the
Mach 10 shock. Inflow and outflow boundary conditions are used
for the left and right boundaries. The unshocked fluid has a density
of \(1.4\)  and a pressure of \(1.\)  The problem was run till \(t=0.2\) 
and the blow-up region around the double Mach stems. The ration of
specific heats \(\gamma =1.4\)  and we set CFL number as \(0.5.\)  The
results in \([0,3]\times [0,1]\)  are displayed for the WENO-JS, WENO-P
and MWENO-P schemes in figures 11, 12 and 13 respectively. The figure
14 shows that the performance of the schemes WENO-JS, WENO-P and MWENO-P
at the Mach stem of the density variable at the final time with several
grid points. It can be clearly seen that MWENO-P resolves better the
instabilities around the Mach stem.
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